Use NInject to initialize several collections

Question

I apologize in advance if this is a dumb question: I am quite new to NInject.

I need to initialize my application with several collections, each having several identical objects. Without IoC, that would look like:

  public ICollection<ICollection<IBusinessObject>> Piles = new ICollection<ICollection<IBusinessObject>>();

    public MyCollectionContainer()
    {
        Piles.Add(new List<IBusinessObject>({ new ObjectA(), new ObjectA()  });
        Piles.Add(new List<IBusinessObject>({ new ObjectB(), new ObjectB()  });
        Piles.Add(new List<IBusinessObject>({ new ObjectC(), new ObjectC()  });
    }

I'd like to instruct NInject to do that job for me, so that a call to Kernel.Get<MyCollectionContainer>() would do the same job as above, with some extra flexibility, of course.

In other words, I want, at bind time, to instruct NInject to

Kernel.Bind<ICollection<ICollection<IBusinessObject>>>().To< /* A list of 3 */>();
Kernel.Bind<IList<IBusinessObject>>().To< /* A List of 2 IBusinessObject */>();
Kernel.Bind<IBusinessObject>().To< /* a different type depending on the container */>();

Side question: Should I better use Kernel.Get<MyCollectionContainer>() or Kernel.Get<ICollection<ICollection<IBusinessObject>>>()

EDIT: While searching for a solution, I tried to define a custom binding for my collections in the model of

Kernel.Bind<IList<IBusinessObject>>()
        .ToConstructor(x => new List<IBusinessObject>(
            x.Inject<IList<IBusinessObject>>())
        );

With an extension method IConstructorArgumentSyntax.InjectMany(int i):

Kernel.Bind<IList<IBusinessObject>>().To<ObjectA>();
Kernel.Bind<IList<IBusinessObject>>()
        .ToConstructor(x => new List<IBusinessObject>(
            x.InjectMany<IList<IBusinessObject>>(2))
        );

public static T InjectMany<T>(this IConstructorArgumentSyntax x, int numberOfInjections)
{
    /* loop */
    {
        x.Inject<T>();
    }
}

Sadly NInject refuses to call x.Inject(); complaining that I've dived too deep into their magic:

System.InvalidOperationException : 
This method is for declaration that a parameter shall 
be injected only! Never call it directly.